Multiply the following complex numbers: $({-5+5i}) \cdot ({4+5i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5+5i}) \cdot ({4+5i}) = $ $ ({-5} \cdot {4}) + ({-5} \cdot {5}i) + ({5}i \cdot {4}) + ({5}i \cdot {5}i) $ Then simplify the terms: $ (-20) + (-25i) + (20i) + (25 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (-25 + 20)i + 25i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (-25 + 20)i - 25 $ The result is simplified: $ (-20 - 25) + (-5i) = -45-5i $